Mostly merry monarch? There’s a slight catch (7)
I believe the answer is:
tiddler
'a slight catch' is the definition.
(small fish)
'mostly merry monarch?' is the wordplay.
'mostly' means to remove the last letter (most but not all of the word).
'merry' becomes 'tiddly' (both can mean slightly drunk).
'monarch?' becomes 'ER' (abbreviation for Elizabeth Regina, British Queen).
'tiddly' with its final letter removed is 'tiddl'.
'tiddl'+'er'='TIDDLER'
'there's' is the link.
(Other definitions for tiddler that I've seen before include "Small fish (or child?)" , "Tiny fish, child" , "Small fry" , "Small fish (colloq,)" , "Small thing" .)